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Simplifying 5(6a + -1b) + -6(8b + -5a) = 0 (6a * 5 + -1b * 5) + -6(8b + -5a) = 0 (30a + -5b) + -6(8b + -5a) = 0 Reorder the terms: 30a + -5b + -6(-5a + 8b) = 0 30a + -5b + (-5a * -6 + 8b * -6) = 0 30a + -5b + (30a + -48b) = 0 Reorder the terms: 30a + 30a + -5b + -48b = 0 Combine like terms: 30a + 30a = 60a 60a + -5b + -48b = 0 Combine like terms: -5b + -48b = -53b 60a + -53b = 0 Solving 60a + -53b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '53b' to each side of the equation. 60a + -53b + 53b = 0 + 53b Combine like terms: -53b + 53b = 0 60a + 0 = 0 + 53b 60a = 0 + 53b Remove the zero: 60a = 53b Divide each side by '60'. a = 0.8833333333b Simplifying a = 0.8833333333b
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